Biomedical Engineering Reference
In-Depth Information
The parameters
s
and
l
are defined by the following two equations:
1
1
1
(15.7)
RC
R C
me
mmm
1
1
1
RC
(15.8)
RC
p
p
p
s
p
p
cannot be directly obtained by exponential decomposition of the
photosignal but it can be recovered by means of deconvolution, using only input param-
eters that can be determined experimentally (
Thus, the time constant
l
,
R
e
,
R
m
,
C
m
,
R
s
). Contrary to the common
practice of curve fitting using adjustable parameters, the present equivalent
circuit model has no freely adjustable parameters. We observed that when
R
e
is compara-
ble to the source impedance of the membrane, the data obtained by means of deconvolu-
tion are more accurate than at other
R
e
values. In fact, individual values of
R
p
and
C
p
can
be so determined. In contrast, a short-circuit measurement can only determine the value
of the product,
R
p
C
p
, but not the individual values of
R
p
and
C
p
. We routinely tuned the
value of
R
e
to optimize the measurements of
R
p
and
C
p
. For this reason, this method is
named the
tunable voltage clamp
(TVC) method [36].
The source impedance of the membrane is much reduced in the high-frequency range
because the chemical capacitance is connected in series to the photoemf. In other words, the
built-in high-pass filter consisting of
R
p
and
C
p
selectively suppresses signal components
representing slower electrical processes and preferentially lets signal components represent-
ing faster processes pass through without attenuation. This is why the DC photocurrent is
usually below the noise level when the AC photocurrent is measured by means of the TVC
method. This is also why an intended short-circuit measurement with a commercial picoam-
meter (input impedance about 100 k
s
,
) can actually be closer to open-circuit than to short-
circuit conditions because the source impedance at high frequency can be easily reduced to
the order of 10 k
(that of
R
p
) [54] (see also discussion in [53] and Section 11 of [29]).
A typical comparison of the prediction of the equivalent circuit with the experimental
measurement is shown in Figure 15.2. The time constant
p
, as obtained by means of decon-
s. A remarkable picture emerges if we identify the reciprocal of this time
constant as the rate constant of the pseudofirst-order reverse electron transfer. In Figure
15.3B, the reciprocal of this time constant is plotted against the concentration of ferrocyanide
at the
oxidant side
. The data fit a straight line that intercepts both axes at the origin. This result
is consistent with the fact that the reverse reaction is a bimolecular second-order reaction.
The slope gives the second-order rate constant of (4.3
volution, is 44
10
7
M
1
s
1
. The agreement
between the predicted and the measured time course of the AC signal motivated us to inves-
tigate the molecular origin of the chemical capacitance and to prove the assumption that
1/
0.5)
p
is actually the pseudofirst-order rate constant of the reverse electron transfer [35].
15.4
Proton as a Charge Carrier: Bacteriorhodopsin Membranes
The investigation of the purple membrane of
H. salinarum
is a natural extension of the
study of the Mg porphyrin membrane. The purple membrane contains a single mem-
brane-bound protein, bR. It is essentially a light-driven proton pump. It exhibits a DC pho-
toelectric signal. However, the unidirectionality of the DC photocurrent is not a
